Abstract — The article considers the research of the passage of the harmonic signals at different frequencies for probing nano-objects to determine the dependence of the frequency range of the probing signal and the range of applicability of the multi-frequency phase method of measuring of the distances at the determination of the size of nano-objects.

Index Terms — Multi-frequency phase method, nano-

object, size of nanoparticles.

I. INTRODUCTION

he rapid development of nanotechnology provides for the monitoring, detection and identification of the

nanoparticles (NPs) and nanotechnology-based materials in the environment in which they can get at their using by human in the industry and at home. To control the life cycle of NPs it is necessary to have instruments that allow to determine the size of nano-objects (NOs) in various medium (air, water, soil).

Measuring of the size of NOs requires the use of certain methods and techniques based on the various physical effects which are inherent to micro- and nanoworld. Size, structure, morphology of NPs are determined by scanning and transmission electron microscopy, tunnel and force microscopy. There are methods for determining the integral characteristics of nanopowder. Each method has own certain advantages and limitations [1,2].

Methods of electronic, tunnel, nuclear microscopy allow determining of the size, shape, degree of agglomeration of NPs, and their structure visually sometimes. But the dependence of the image from a mathematical model of image reconstruction does not allow the study of large samples of NPs. As well as the characteristics of accuracy are largely dependent on the degree of preparedness of the operator to conduct such measurements.

X-ray diffraction methods allow determining of the average characteristics of the powders, but the adequacy of the results

is largely dependent on the mathematical apparatus for solving the inverse problem of X-ray line profile analysis.

Dynamic light scattering method is promising. It allows to define the characteristics of a great number of NPs with a wide size distribution. The main disadvantages of sizing are the dependence of the results of the adequacy of the mathematical model on the correlation analysis, the complexity of the selection of the dispersion medium and agglomeration of particles in the test suspensions. [1,2]

It is proposed to use an alternative method for the direct study of NPs size and determination of the threedimensional structure of the suspensions of NPs with the use of scanning of the area.

II. MAIN PART Direct measurement of size involves the use of probing

radiation with the parameters which will be reference for determining of the size.

Direct methods for measuring of distances and sizes are used in the radar scatterometry, ultrasound radiography and defectoscopy. These methods are based on the use of probing radio or ultrasonic radiation. The distances are determined by time delays or phase shifts of the reflected signals.

The most accurate method is a multi-frequency phase method of the measuring of distances. This method involves the probing of objects by harmonic signals in the definite range of frequencies with the fixed frequency step. The signals are reflected from the object of measurement and returned to the point of emission. In this case all reflected signals are harmonic and, according to the principle of superposition, are superimposed on each other. It leads to transmission of one harmonic signal in the point of radiation at each frequency which can be described by the expression ( ia - the amplitude of the total signal at the i-th frequency;

i - phase shift of the total signal at the i-th frequency; 1a -

amplitude of the signal reflected from the first object; 1 - phase shift of the reflected signal from the first object):

ni ji

njijij

i eaeaeaea ...21

21 , (1)

Vitalii Liubchyk1, Svitlana Karvan2, and Georgiy Paraska3

1Department of Radio Engineering and Communications, Khmelnitsky National University, Khmelnitsky, Ukraine

2Department of Chemistry & Experimental Laboratory of Industrial Chemicals, Khmelnitsky National University, Khmelnitsky, Ukraine

3Department of Machines and Apparatus, Khmelnitsky National University, Khmelnitsky, Ukraine Email: liubchyk.v@gmail.com, karvan@ukr.net, nauka@mailhub.tup.km.ua

Model of Transmission of Probing Signals in the Study of Nano-objects

T

Getting of the total harmonic signal at the first frequency at the reflection of the probe signal from the three objects is shown in Figure 1. The amplitudes of the reflected signals are commonly the same, and all objects of measurement are at equal distances. The harmonic probing signal at a first frequency has the wavelength which is twice larger than the maximum determined distance.

The increasing of frequency by twice leads to reduction of the wavelength by half resulting in a change of amplitude and phase ratio of the total probing signal. Figure 2 shows the receipt of the total harmonic signal at a second frequency.

The amplitude and phase shift change is not linear when comparing the graphs the total reflected signal at the first and second frequency. [3]

Through measuring the amplitudes and phase shifts of the total reflected signals at several frequencies, whose number is determined by measuring the number of objects, we can write the system of equations ( ib - the vector of the total reflected

signals, ir - the value of mathematical transformations of the vectors of signals reflected from each object):

n

n

n

nnn

nn

nn

nn

nn

nn

nn

b

bb

r

rr

bbbb

bbbbbbbb

2

1

1

2

1

12112

22122

1

1111

32

11

1121

......11...

...............11...

11...

,

(2)

After all mathematical transformations of the system (1) we have obtained the values of the vectors of signals reflected from each object. This in turn allows to obtain the values of the phase shifts of these signals and, consequently, the distance to each object.

The frequencies are located in the area from low to high frequencies at the measurements in radar, radiography, reflectometry. The measured distances are comparable with the wavelengths of tens or hundreds of kilometers to the units and tens of meters. But when measuring of the size of NOs

the wavelength of the probing signals should be commensurate with the distances in units of mm or less. Therefore it is necessary to determine the frequency at which the finding of the size of NOs will be possible.

Distribution of NPs in suspension in depth will have the size of a nanometer range from a few nanometers to several micrometers. Thus, the unambiguous measurement of the minimum phase shift min will be provided by the wavelength of the probing radiation with value according to the relation ( minl - the minimum measurable distance, min - the minimum phase shift):

min

minmin

4 l

, (3)

To provide an unambiguous measurement of the maximum

measured distance maxl , we need to choose a wavelength

determined by the expression ( max - the maximum phase shift):

max

maxmax

4 l

, (4)

Minimum measuring distance is determined by the size of

the NPs. The maximum measuring distance is given by way of sample preparation.

Thus, if the thickness of the sample does not exceed 10 m at the maximum phase shift which allows the ensuring of the unambiguous measurement of 180°, then

66

max 104010104

(м), (5)

and the lower limit of the frequency range is

Fig.1. Formation of the total reflected signal at the first frequency: а) The graph of the probing signal b) The graph of the reflected signal

Fig. 2. Formation of the total reflected signal at a second frequency: а) Graph of the probe signal; b) Graph of the reflected signal.

126

8

max

105.71040103

cf н

(Гц) (6)

To ensure measurement of the minimum size of 10 nm at the minimum phase shift of 5° the wavelength of the probing radiation will be

9

9

min 101440361

10104

(м), (5)

the upper limit of the frequency range is

12

9

8

min

103.208101440

103

cf в (Гц) (6)

Thus, the frequency range of the probing radiation must be

specified in the range from 7.5 to 208.3 THz. [4] This frequency range relates to the infrared range. It is located above the radio band. The signals of the band are formed by microwave devices - magnetrons, and others. It is also placed below the optical range. Signals in this range are formed by quantum devices. Thus, there are certain difficulties in the formation of the probing radiation and processing the reflected signals. Для The modulation techniques of IR monochromatic radiation can be applied for the generation of signals in the IR range in a wide band of the frequency. In this case, the signals will be generated in a given range of frequencies from the lower to the upper boundary. Then the mathematical model of the signals will be described by the system of equations:

nf

nf

nf

nnfn

nfn

nfnf

nfn

nfn

ff

nfn

nfn

ff

н

н

н

нннн

нннн

нннн

b

bb

r

rr

bbbb

bbbbbbbb

2

2

1

2

1

12112

22122

1

1111

32

11

1121

......11...

...............11...

11...

. (7)

There are two necessary conditions for the uniqueness of the measurements:

- The wavelength at a first frequency is twice larger than the maximum measured distance:

max2 L

нf ; (8)

- The number of probing frequencies is twice larger than

the number of measured objects:

... 2 обзч NN (9) The errors of the measurement of the size of conductive NOs on the basis of radiation in the infrared range of the spectrum will be determined by the wavelength of the probing signals, errors of the measurements of the reflected signals and the methods of mathematical processing of the primary measurements. The analysis of the method of measurement

and mathematical transformations has allowed to obtain the mathematical expression for the measurement error:

cc

cfAcond

fc

fcl

n

112)(

arg4

arg4

1max

. (10)

Analysis of this expression shows that the error of distance measurement depends on the initial frequency of the measuring signal and the frequency range of measurement signals. [5] The last statement requires explanation. Since the value of the number of conditionality of the matrix depends on the values of the coefficients of the matrix, the choice of frequency range can define such correlation coefficients that the number of conditionality will be minimal. Thus, multifrequency phase method of measuring distances should be completed by the last step, specifically, the test conditions of the minimum of distance error. The test should be carried out in a cycle. Varying specific frequency band of the probing signal is found and the error are compared with errors obtained in the previous step. The error measurement process ends after reaching of the minimum value.

Structural scheme of determination of NOs. The experimental plant includes a laser light source 1, modulator 2, four semi-transparent mirrors 3, broadband signal generator 4, the register of radiation and interferometer 5, computer system 6, test sample with NOs 7. Laser radiation is modulated by the modulator at the amplitude. Then, it passes through two semi-transparent mirrors and goes to the test sample. The reflected signals from first surface of NPs and from second surface, which are superposed by each other, have formed the summarized signal. This signal is reflected in the opposite direction. After reflecting from the semi-transparent mirrors, it goes to the register of the radiation and the interferometer. The amplitude-frequency and phase-frequency characteristics are determined by the measuring of the amplitudes of the reflected signals and phase difference at different harmonic modulation signals. As a result of their mathematical calculations the size of the NPs is determined.

III. CONCLUSION Measurement of nanoscale objects is a difficult task and

time-consuming. Various measurement methods do not allow to determine the size with high accuracy. The main problem is that the measurements are usually agglomerates NPs, not

1 2

3

3

3

3

5 6

7

4

Fig. 3. Structural scheme of determination of NOs

the objects themselves. This is due to the fact that indirect measurements are carried out. The measurements of particle scattering, light emission, etc. which determine the values of particle size distribution.

To overcome this problem are encouraged to use the direct method of measurement. The method consists in probing NPs laser light whose wavelength is comparable with the measured dimensions. In this case, the reflected signals from each nanoobject can be used to find sizes. It is proposed to use the phase method of measurement of dimensions to many objects. Preliminary calculations have allowed to determine the frequency range of the probing radiation. It is determined from the condition for the resolution of the distance and the thickness of the prepared solution with nano-objects. To ensure resolution of 1 nm in size in the solution layer, which is 1 mm, frequency range of the probing radiation lies in the range from several to hundreds of terahertz, which relates to short-wave infrared light and medium field.

REFERENCES

[1] C. P. Poole Jr., F. J. Owens, Introduction to nanotechnology, USA: A Willey Interscience publ., 2003, pp. 388.

[2] M. Wilson, K. K. G. Smith, M. Simmons, B. Raguse, Nanotechnology : basis science and emerging technologies, Sydney : A CRC Press Company, 2002, pp. 263.

[3] G. B. Paraska, O. M. Shinkaruk, V. R. Liubchik, “Theoretical basis of phase measurement to several objects,” Electronics and Communications, 3, pp. 82-86, 2010.

[4] O. Shinkaruk, V. Liubchik, “Multy-phase metods of measuring distances, ” in Scientific basis of modern technology: experience and prospects, edited by Y. I. Shalapko and L. A. Dobrzanski, Khmelnitsky, 2011, pp. 530-536.

[5] O. Shinkaruk, V. Liubchik, Т. Dement`ev “Investigation of the potential accuracy and resolution phase many frequency method of measuring distances” Electronics and Communications, 3, pp. 78-82, 2011.